There are many ways a time way s a time travel can work in fiction. Here are some of them:

Time loop: Basically, you've already changed the past and you caused the very thing you wanted to prevent from happening in the first place.
This type of time travel is generally not very satisfying, whether you see it coming or not.

Timeline superposition: Basically, multiple outcomes exist simultaneously. Explanation here.
This type of time travel is not often seen as it's kind of a new solution.

Alternate timelines: Time traveling backwards has to create a new timeline. So you can kill your own grandfather but in the original timeline nothing changes so no paradox is created.
This type usually works well if you want a time travel to get something done.

You know what, Screw it. Time travel makes its own rules This type of time travel is the one where the logic is thrown out of window and rules of time travel are not consistent. For an example, you can see houses disappearing because meanwhile in the past, someone is blowing them up.
This type of time travel is silly, but allows most liberties to be taken with the plot. It's just that the plot must let know the audience that the effects of time travel doesn't make much sense in that kind of series.

My pick is good old alternative timeline. Never liked the other ways to be honest, and I despise to consider the current system (as written in one of those threads about Timelock holding something and bla bla bla) canon as well.